Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C26 |
| direct product | D32×#1020 |
| Fitting, socle | C24×C32 ⋊ C22×D3 |
| derived | C32×C22⋊A4 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C22⋊A4 | C23 |
| Fitting, socle | C24×C32 | C22×D3 |
| LCS | G ▷ C32×C22⋊A4 | |
| UCS | C1 | |
6076 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 6076 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
90 conjugacy classes — view the full character table.
| maximal subgroup of | D32×A4⋊S4, D3×C3⋊D3×#1020, D3×#13181837, … |
| maximal normal subgroup of | D32×#1020⋊C2, #72241545 |
| maximal quotient of | D3×C3⋊D3×#1020, D3×#13181837 |
Past the SmallGroups library coverage — no SmallGroups id.